THE CONSTRUCTION OF WAVELET-BASED TRUNCATED CONICAL SHELL ELEMENT USING B-SPLINE WAVELET ON THE INTERVAL

Based on B-spline wavelet on the interval （BSWI）, two classes of truncated conical shell elements were constructed to solve axisymmetric problems, i.e. BSWI thin truncated conical shell element and BSWI moderately thick truncated conical shell element with independent slopedeformation interpolation. In the construction of wavelet-based element, instead of traditional polynomial interpolation, the scaling functions of BSWI were employed to form the shape functions through the constructed elemental transformation matrix, and then construct BSWI element via the variational principle. Unlike the process of direct wavelets adding in the wavelet Galerkin method, the elemental displacement field represented by the coefficients of wavelets expansion was transformed into edges and internal modes via the constructed transformation matrix. BSWI element combines the accuracy of B-spline function approximation and various wavelet-based elements for structural analysis. Some static and dynamic numerical examples of conical shells were studied to demonstrate the present element with higher efficiency and precision than the traditional element.

Nonlinear vibration of functionally graded graphene platelet-reinforced composite truncated conical shell using first-order shear deformation theory

In this study,the first-order shear deformation theory(FSDT)is used to establish a nonlinear dynamic model for a conical shell truncated by a functionally graded graphene platelet-reinforced composite(FG-GPLRC).The vibration analyses of the FG-GPLRC truncated conical shell are presented.Considering the graphene platelets(GPLs)of the FG-GPLRC truncated conical shell with three different distribution patterns,the modified Halpin-Tsai model is used to calculate the effective Young’s modulus.Hamilton’s principle,the FSDT,and the von-Karman type nonlinear geometric relationships are used to derive a system of partial differential governing equations of the FG-GPLRC truncated conical shell.The Galerkin method is used to obtain the ordinary differential equations of the truncated conical shell.Then,the analytical nonlinear frequencies of the FG-GPLRC truncated conical shell are solved by the harmonic balance method.The effects of the weight fraction and distribution pattern of the GPLs,the ratio of the length to the radius as well as the ratio of the radius to the thickness of the FG-GPLRC truncated conical shell on the nonlinear natural frequency characteristics are discussed.This study culminates in the discovery of the periodic motion and chaotic motion of the FG-GPLRC truncated conical shell.

Buckling analysis of functionally graded material(FGM) sandwich truncated conical shells reinforced by FGM stiffeners filled inside by elastic foundations

An analytical solution for buckling of an eccentrically stiffened sandwich truncated conical shell is investigated. The shell consists of two functionally graded material （FGM） coating layers and a core layer which are metal or ceramic subjected to an axial compressive load and an external uniform pressure. Shells are reinforced by stringers and rings, in which the material properties of shells and stiffeners are graded in the thickness direction following a general sigmoid law distribution. Two models of coated shell-stiffener arrangements are investigated. The change of the spacing between stringers in the meridional direction is taken into account. A couple set of three-variable- coefficient partial differential equations in terms of displacement components are solved by the Galerkin method. A closed-form expression for determining the buckling load is obtained. The numerical examples are presented and compared with previous works.

Couple stress-based nonlinear primary resonant dynamics of FGM composite truncated conical microshells integrated with magnetostrictive layers

The size-dependent geometrically nonlinear harmonically soft excited oscillation of composite truncated conical microshells(CTCMs)made of functionally graded materials(FGMs)integrated with magnetostrictive layers is analyzed.It is supposed that the FGM CTCMs are subjected to mechanical soft excitations together with external magnetic fields.An analytical framework is created by a microstructuredependent shell model having the 3rd-order distribution of shear deformation based on the modified couple stress(MCS)continuum elasticity.With the aid of the discretized form of differential operators developed via the generalized differential quadrature technique,a numerical solution methodology is introduced for obtaining the couple stress-based amplitude and frequency responses related to the primary resonant dynamics of the FGM CTCMs.Jump phenomena due to the loss of the first stability branch and falling down to the lower stable branch can be seen in the nonlinear primary resonance of the FGM CTCMs.It is demonstrated that the hardening type of nonlinearity results in bending the frequency response to the right side,and the MCS type of size effect weakens this pattern.Moreover,for higher material gradient indexes,the hardening type of nonlinearity is enhanced,and the MCS-based frequency response bends more considerably to the right side.

Influence of elastic foundations and carbon nanotube reinforcement on the hydrostatic buckling pressure of truncated conical shells

In this study,the effects of elastic foundations(EFs)and carbon nanotube(CNT)reinforcement on the hydrostatic buckling pressure(HBP)of truncated conical shells(TCSs)are investigated.The first order shear deformation theory(FOSDT)is generalized to the buckling problem of TCSs reinforced with CNTs resting on the EFs for the first time.The material properties of composite TCSs reinforced with CNTs are graded linearly according to the thickness coordinate.The Winkler elastic foundation(W-EF)and Pasternak elastic foundation(P-EF)are considered as the EF.The basic relations and equations of TCSs reinforced with CNTs on the EFs are obtained in the framework of the FOSDT and solved using the Galerkin method.One of the innovations in this study is to obtain a closed-form solution for the HBP of TCSs reinforced with CNTs on the EFs.Finally,the effects of the EFs and various types CNT reinforcements on the HBP are investigated simultaneously.The obtained results are compared with the results in the literature,and the accuracy of results is confirmed.

NONLINEAR STABILITY OF TRUNCATED SHALLOW CONICAL SANDWICH SHELL WITH VARIABLE THICKNESS

The theory of nonlinear stability for a truncated shallow conical shell with variable thickness under the action of uniform pressure was presented. The fundamental equations and boundary conditions were derived by means of calculus of variations. An analytic solution for the critical buckling pressure of the shell with a hyperbolically varying thickness is obtained by use of modified iteration method. The results of numerical calculations are presented in diagrams, which show the influence of geometrical and physical parameters on the buckling behavior.

Buckling Analysis of FG Porous Truncated Conical Shells Resting on Elastic Foundations in the Framework of the Shear Deformation Theory

In this article,an analytical method is proposed to analyze of the linear buckling behavior of the FG porous truncated conical shells subjected to a uniform axial compressive load and resting on the Pasternak elastic foundation.The material properties including Young’s modulus,shear modulus and density are assumed to vary in the thickness direction.Three types of FG porous distributions including symmetric porosity distribution,non-symmetric porosity and uniform porosity distribution are considered.The governing equations of the FG porous truncated conical shells are obtained by using the first-order shear deformation theory(FSDT).With the help of the Galerkin method,the expressions for critical buckling loads are obtained in closed forms.The reliability of the obtained results is verified by comparing the present solutions with the published solutions.Finally,the numerical results show the effects of shell characteristics,porosity distribution,porosity coefficient,and elastic foundation on the critical buckling load.

轴向拉力及静水压力作用下多孔石墨烯增强截锥壳的屈曲特性研究

为研究轴向拉力与静水压力作用下多孔石墨烯增强截锥壳的屈曲特性,基于泡沫金属材料参数的关系和修正的Halpin-Tsai模型,计算了不同孔隙和石墨烯分布的石墨烯增强复合材料的物性参数。利用经典薄壳理论建立了截锥壳屈曲控制方程,并用Galerkin积分法求得了屈曲临界荷载的解析解,根据数值结果讨论了孔隙、石墨烯和截锥壳几何尺寸等因素对材料临界屈曲荷载的影响。结果表明,石墨烯作为增强材料可显著提升壳体的抗屈曲性能,且其抗屈曲能力随着石墨烯含量增加而提高;当壳体表层孔隙少且石墨烯含量高时,截锥壳的抗屈曲能力更好;另外,截锥壳尺寸也会对其抗屈曲性能造成影响。

Winkler弹性介质中多孔功能梯度材料截锥壳的弯曲

弹性介质中板壳结构的力学特性研究,大都假设结构体在变形过程中始终与介质紧密接触。为研究可脱离的Winkler弹性介质中含孔隙功能梯度材料截锥壳在环向荷载作用下的弯曲问题,以陶瓷材料质量分数、体积指数和孔隙率为控制参数,根据混合律计算含均匀孔隙功能梯度材料的物性参数。基于Donnell经典薄壳理论和Hamilton原理,建立Winkler弹性介质和环向荷载共同作用下截锥壳的平衡方程和变形协调方程。考虑锥壳两端简支边界条件,采用Galerkin积分法求解得到截锥壳弯曲挠度的解析解。研究在弹性介质与壳体接触和脱离两种情况下,孔隙率、功能梯度材料组成和截锥壳尺寸等因素对壳体挠度值的影响。结果表明,截锥壳挠度值随着孔隙率、体积指数、壳体长径比、径厚比和半锥角的增大而增大,随着陶瓷质量分数的增大而减小。截锥壳与Winkler弹性介质接触时的挠度值比脱离时小,这是因弹性介质对壳体有一定的反作用力。在截锥壳母线方向上,其中部的挠度值较大,而由中部到两端的挠度值逐渐减小;在截锥壳环向方向上,其挠度值呈现周期变化。分析多孔FGM截锥壳在弹性介质和环向荷载作用下的弯曲问题,为FGM截锥壳在工程领域中的应用提供了理论基础。

功能梯度截顶圆锥壳的热弹性弯曲精确解

研究了功能梯度材料截顶圆锥壳在横向机械载荷与非均匀热载荷同时作用下的变形问题.基于经典线性壳体理论推导出了以横向剪力和中面转角为基本未知量的功能梯度薄圆锥壳轴对称变形的混合型控制方程.假设功能梯度圆锥壳的材料性质为沿厚度方向按照幂函数连续变化的形式.然后采用解析方法求解,得到了问题的精确解.分别就两端简支和两端固支边界条件,给出了圆锥壳的变形随其载荷、材料参数等变化的特征关系曲线,重点分析和讨论了载荷参数与材料梯度变化参数对变形的影响.

旋转壳的数值传递函数方法

应用数值传递函数方法建立了一种用于分析旋转壳静力、动力响应的截锥壳单元。在本方法中，单元的位移在环向展开为Fourier级数的形式，应用薄壳理论可以得到解耦的微分方程。通过Laplace变换可以将方程转化为频域内的常微分方程，将其表示为状态空间形式后，可以应用数值传递函数方法求解。对复杂的系统可以应用与有限元类似的方法，划分多个单元组合求解。文中给出了几种旋转壳的动力、静力问题的数值算例，并与其它方法进行了比较，表明本文方法具有精度高、计算方便等特点。

变厚度夹层截顶扁锥壳的非线性稳定性分析

对具有变厚度夹层截顶扁锥壳的非线性稳定问题进行了研究· 利用变分原理导出表层为等厚度而夹心为变厚度的夹层截顶扁锥壳的非线性稳定问题的控制方程和边界条件 ,采用修正迭代法求得了具有双曲型变厚度夹层截顶扁锥壳的非线性稳定性问题的解析解 ,得到了内边缘与一刚性中心固结而外边缘为可移夹紧固支的变厚度夹层截顶扁锥壳临界屈曲载荷的解析表达式 ,讨论了几何参数和物理参数对壳体屈曲行为的影响·

区间B样条小波薄壳截锥单元构造

利用区间B样条小波的尺度函数作为有限元插值函数,从轴对称壳的能量泛函出发,由变分原理导出了单元刚度矩阵和载荷列阵,构造了区间B样条小波薄壳截锥单元。区间B样条小波单元同时具有B样条函数数值逼近精度高和多种用于结构分析的变尺度基函数的特点。数值算例表明:与传统截锥单元相比,本文构造的小波单元具有求解精度高、单元数量和自由度少等优点。

截锥壳驻波颤振极限环研究

为研究大挠度非线性位移-应变条件下,截锥壳非线性颤振响应特性,基于活塞理论的气动力法,建立了超音速截锥壳非线性气动弹性运动方程.采用微分求积法对方程进行离散化变换,在驻波颤振假设下,用低阶固有模态缩减自由度数,模拟驻波颤振极限环幅值及随气动参数的变化过程.结果表明:前6阶模态下缩减自由度数,可获得较为精确的解;当气动压力参数增大至7 312时,系统经过Hopf分叉后进入极限环运动.

偶极子源与力激励作用下截顶锥形壳振动与声辐射研究

螺旋桨噪声是舰船辐射噪声的主要组成部分,采用有限长截顶锥形壳模拟潜艇艉部,根据螺旋桨噪声产生机理,对比分析了集中力激励与偶极子源激励下锥形壳产生的辐射噪声,并讨论了激励作用位置对壳体振动与辐射噪声的影响。结论显示力激励作用引起的壳体的振动与声辐射要大于偶极子源作用下的情况;当激励施加在锥形壳体截面的中心位置时,壳体在低频时的振动与声辐射要小于激励施加在截面非对称位置处的情况。

截锥壳颤振分析的微分求积法

引入微分求积法（Differential Quadrature Method,简称DQM）对截锥壳气动弹性方程离散,采用一阶活塞理论气动力,运用特征值分析方法求解系统的颤振临界动压。研究了半顶角、径厚比、长径比等几何参数对颤振临界动压的影响。结果表明,DQM求解截锥壳气动弹性方程具有良好的精度和计算效率,结构产生1阶~2阶耦合型颤振的最低临界动压对应的周向波数较大,并因几何参数而异;颤振临界动压参数随半顶角的增大而减小,随着径厚比的增大而增大,随长径比的增大而减小。

温度依赖热弹性功能梯度截顶圆锥壳的弯曲精确解

研究功能梯度材料截顶圆锥壳在横向机械载荷与非均匀热载荷同时作用下的变形问题.基于线性壳理论建立问题的混合型控制方程,其中考虑组分材料物理性能参数的温度依赖性,并且假设功能梯度圆锥壳的材料性质为沿厚度方向按照幂函数连续变化的形式.采用解析方法求解,得到问题的Bessel函数形式的全部精确解.分别就两端简支和两端固支边界条件,给出功能梯度圆锥壳的变形随其载荷、材料参数等变化的特征关系曲线,分析和讨论热载荷参数、材料梯度变化参数和物性参数的温度依赖性对变形的影响.

基于渐近传递函数解的截锥壳单元

普通截锥壳单元是分析旋转壳结构的常用单元,但应力计算的精度较差;而渐近传递函数解在圆锥壳的应力分析方面具有很高的计算精度。本文针对一般截锥壳单元应力计算精度不高的缺点,将传递函数法与有限元法进行结合,以圆锥壳的渐近传递函数解为插值函数,直接构造了一种高精度的截锥壳单元。该单元位移插值模式满足相容性和完备性要求,并具有力学概念清楚、计算精度高等特点。数值算例表明,采用该单元进行圆锥壳的内力和自由振动频率分析,计算效率明显高于普通截锥壳单元。

均布侧压下刚性圆顶锥壳的精确解

应用薄壳理论获得了刚性圆顶锥壳在均布侧压作用下的精确解，所用混合型控制方程适用于常见锥度范围内一般锥壳的轴对称弯曲变形。

截顶圆锥壳屈曲载荷的灰色预测

将灰关联分析方法引入极值性失稳破坏的研究,建立了根据实测压力～应变数据预测结构破坏载荷的新方法,采用该方法预测了承受外压的环肋截顶圆锥壳的破坏载荷,并通过破坏性试验和有限元分析结果,验证了本方法的实用性与有效性.